NSW Bureau of Crime
Statistics and Research
Bureau Brief
Issue paper no. 97
August 2014
The effect of suspended sentences on imprisonment
Patricia Menéndez and Don Weatherburn
Aim: To see whether the introduction of suspended sentences reduced the number of offenders receiving a fulltime sentence of imprisonment
Method: The number of persons receiving a prison sentence was regressed against the number receiving a
suspended sentence while controlling for changes in the total number of proven offenders and the monthly
variability using multiple linear regression with ARIMA errors. The data set used for the analysis consisted of the
monthly number of persons imprisoned, persons given a suspended sentence and proven offenders from January
2002 to December 2013.
Results: Every 10 additional offenders given suspended sentences was associated with an extra 3-4 offenders
sent to prison.
Conclusion: Although suspended sentences were introduced as an alternative to prison, they appear to have had
the opposite effect.
Introduction
Figure 1. Time series for the total number of proven
offenders (PO), total number receiving a
sentence of imprisonment (FTP) and total
number given suspended sentence (SS)
PO
SS
300
400
500
600
600
FTP
In an earlier report in this series, McInnis and Jones (2010) found
that the increase in the use of suspended sentences had not
been accompanied by a reduction in the rate of imprisonment.
Instead, it had been accompanied by a reduction in the use of
other non-custodial penalties, most notably community service
orders (CSOs). Over the period between 1999 and 2008, the
percentage of CSOs imposed in the Local Courts fell from 20.4
per cent to 11.5 per cent. In the year prior to the introduction
of suspended sentences, CSOs accounted for 9.1 per cent of
all penalties imposed by the Higher Criminal Courts. By 2008,
800
10007000
9000
11000
Suspended sentences were introduced in NSW in April 2000.
They proved extremely popular. Between 2000 and 2013, the
number of suspended sentences imposed by adult courts in
NSW rose by more than 180 per cent (from 1,849 to 5,224) (see
Figure 1). Under s.12 of the Crimes (Sentencing Procedure) Act
(1999), suspended sentences of imprisonment should only be
imposed where a sentence of full-time imprisonment would
normally be appropriate. Other things being equal, then, we
would expect an increase in the use of suspended sentences
to be accompanied by a reduction in the use of full-time
imprisonment.
2002
2004
2006
2008
Time
1
2010
2012
2014
the use of CSOs by the NSW Higher Criminal Courts had all but
ceased.
receiving a suspended sentence. To deal with the problem of
autocorrelation so often found in time series analysis, and to
avoid problems of spurious regression relationships, we test
our hypothesis using multiple linear regression with ARIMA
errors (Box, Jenkins, Reinsel 2013). Our model of the number
of offenders imprisoned is therefore given by:
In discussing their findings, McInnis and Jones (2010) raised the
possibility that the increased use of suspended sentences, far
from reducing the use of imprisonment, might actually increase
it. As they put it:
yt = β0 + β1 x1 + β2 x2 + d1 I1 + . . . d11 I11 + ηt
ηt ∼ ARIM A(0, 1, 1)
“This imposition of suspended custodial sanctions on
offenders who would otherwise have received a noncustodial sanction has potentially serious implications
for imprisonment rates over the longer term. The risk
of imprisonment is probably higher for breaching
the conditions of a suspended sentence than it is
for breaching a good behaviour bond or a CSO. One
unintentional consequence of increasing the use of
suspended sentences is that a greater number of
offenders may be drawn into the prison population.”
(McInnis & Jones 2010, p. 4)
where:
x1 = the number of suspended sentences;
x2 = the total number of persons sentenced;
Ii = monthly dummies i=1, ... ,11; and
ηt = an ARIMA error term to capture autocorrelation in the series.
Our interest lies in the sign and magnitude of β 1, which
measures the effect of suspended sentences on the number
of persons imprisoned. If increasing the number of suspended
sentences has the effect of decreasing the imprisonment rate,
we expect the sign to be negative. Although equations (1) and
(2) identify the model being tested, because the series being
analysed were not stationary, the model was estimated in
differences.
The purpose of this brief is to see whether the concerns
expressed by McInnis and Jones (2010) have been realised.
Specifically, we report the results of a study designed to test the
hypothesis that the introduction of suspended sentences has
contributed to a growth in the number of convicted offenders
receiving a sentence of imprisonment.
Method
The contemporaneous relationship between the number of
sentences of full-time imprisonment, the suspended sentences
and the total number of proven offenders in the model was
investigated via the cross-correlation function. Checking of
model assumptions was carried out by looking at the residuals
of the fitted model. The independence of the residuals was
checked by examining their autocorrelation and partial
autocorrelation functions, and by using the Ljung-Box test
(Ljung and Box, 1978) based on the first 24 autocorrelations
(H0: Residuals are independent). The normality assumption for
the residuals was tested using the Shapiro-Wilk test (Shapiro
and Wilk, 1965) (H0: Residuals are normally distributed). The
significance level for all tests in this analysis was set at α = 0.05.
Data
Data for the study consisted of monthly counts between 2002
and 2013 of (a) the total number of people convicted in NSW
Local, District and Supreme (Higher Criminal) Courts, hereafter
referred to as the number of proven offenders (b) the number
receiving a suspended sentence and (c) the number receiving a
full-time sentence of imprisonment. January 2002 was chosen
as the start point for analysis because, although suspended
sentences were introduced in April 2000, the monthly number
imposed remained quite low through 2000 and 2001. Note that
we count a person as a proven offender if one or more offences
are proved against them, even if no conviction is recorded and
the offender placed on a bond.
Results
Analysis
Before presenting the results of the analysis it is useful to
examine trends in the variables examined in the study.
1 of persons
Figure 1 shows time series plots of the number
receiving a full-time sentence of imprisonment, the number
receiving a suspended sentence and the number of proven
offenders. All three series show a rising trend between 2002
and around 2009 and a falling trend until 2012. At this point,
the total number sentenced continues to fall but the number
given a prison sentence or a suspended sentence rises again.
The question we seek to address is whether the number of
sentences of full-time imprisonment increased in response
to the growth in the number of suspended sentences. In
examining this question we need to control for the total
number of proven offenders because an increase in this
number could drive up both the number of persons receiving
suspended sentences and the number receiving a sentence of
full-time imprisonment. We also need to control for seasonal
variation in the number of proven offenders and the number
of suspended sentences. To meet these concerns, we model
the relationship between the monthly number of persons
receiving a sentence of full-time imprisonment against the
number receiving a suspended sentence, while controlling for
the monthly number of proven offenders and seasonal variation
in both the number of proven offenders and the number
Figure 2 presents scatterplots of the relationship between
first differenced series for the dependent and independent
variables. The terms PO, FTP and SS refer, respectively, to the
total number of proven offenders, the total number receiving
a sentence of imprisonment and the total number given a
suspended sentence. Each panel shows a scatterplot in which
the y-axis is the change in the variable listed in the same row
2
Figure 2. Pairs plot exhibiting the relationships for the first differenced time series between PO, FTP and SS
−100
0
100
200
1000
2000
−200
100
200
−2000
−1000
0
PO
50
100
150
−200
−100
0
FTP
−2000
−1000
0
1000
2000
−150
and the x-axis is the change in the variable listed in the same
column. The middle scatterplot on the top row, for example,
plots the change in the total number of proven offenders
against the change in the number given a prison sentence. The
panel to the right plots the total number of proven offenders
against the number given a suspended sentence. The panel
on the right hand side of the middle row plots the number
given a prison sentence against the number given a suspended
sentence.
−100
−50
0
50
100
150
−150 −100
−50
0
SS
Residual checks for the fitted model are shown in Figure 3.
The residuals of the fitted model fulfilled the assumptions of
independence, as shown by the ACF and PACF in the figure, and
as confirmed by the Box-Ljung test p-value of 0.93. As noted
earlier, the normality assumption was checked via the ShapiroWilk test. The test gave a p-value of 0.2, indicating that the
Table 1. Results for the multiple linear regression with
ARIMA errors for modelling FTP
There are two key points to note about the scatterplots. The
first is that, as the total number of proven offenders increases,
so too does the number receiving a prison sentence. This
underscores the need to control for the total number of proven
offenders. The second is that, as the number given a suspended
sentence increases, the number given prison sentence rises
also. In order to further investigate the relationship between
the total number receiving a sentence of imprisonment (FTP)
with the total number of proven offenders (PO) and the total
number given a suspended sentence (SS), we study the crosscorrelations between the series. To avoid spurious relationships
due to the non-stationarity nature of the series, we calculated
the cross-correlations (at different lags) between the prewhitened time series for FTP, PO and SS.
Estimates Coefficients
The cross-correlations results confirm a very strong
contemporaneous relationship between the variables. The
contemporaneous (significant) cross-correlation values (i.e. the
cross-correlation values at lag 0) were 0.55 for FTP and PO, and
0.52 for FTP and SS. This provides prima facie evidence that the
rise in suspended sentences has brought with it a rise in the
number entering prison.
t-statistics
p-values
(2 sided test)
SS
0.36
0.10
3.71
0.00
PO
0.05
0.01
6.71
0.00
Jan
-184.13
16.87
-10.92
0.00
Feb
-76.83
18.60
-4.13
0.00
Mar
-39.49
19.65
-2.01
0.05
Apr
-57.50
16.99
-3.38
0.00
May
-30.67
21.53
-1.42
0.16
Jun
-42.81
17.52
-2.44
0.02
Jul
-92.42
17.15
-5.39
0.00
Aug
-47.63
16.76
-2.84
0.01
Sep
-55.55
16.57
-3.35
0.00
Oct
-39.11
16.50
-2.37
0.02
Nov
-12.59
16.61
-0.76
0.45
ma1
-0.72
0.06
-11.32
0.00
loglikelihood = 716.76
AIC = 1463.52
3
SD
Figure 3. ACF, PACF, histogram and Normal QQ-plots for the residuals of the fitted multivariate
ARIMA regression model
Residuals ACF
Residuals PACF
Residuals ACF
0.05
Partial ACF
Partial
ACF
−0.15
−0.05 0.00
0.4
−0.2
0.0
0.2
ACF
ACF
0.6
0.10
0.8
0.15
1.0
Residuals ACF
0.0
0.5
1.0
1.5
0.5
1.0
Lag
Lag
1.5
Lag
Lag
Residuals QQ−plot
Residuals
QQ-plot
50
0
Sample Quantiles
Sample
Quantiles
−50
20
15
0
5
10
Frequency
Frequency
25
30
100
Residuals histogram
Residuals
histogram
−100
−50
0
50
100
−2
Residuals
Residuals
−1
0
1
2
Theoretical Quantiles
Theoretical
Quantiles
Discussion
assumption was met. The normality of the residuals can be also
seen in the residuals histogram and Normal QQ-plots (which
compare the theoretical quantiles of the Normal distribution
with the quantiles of the residuals).
The suspended sentence has been described by some as a
‘Sword of Damocles’ (Bartels 2007) that offers the promise
of deterrence without the costs associated with actually
imprisoning an offender. Research (Weatherburn & Bartels
2008) has shown that suspended sentences are no more
effective in reducing the risk of re-offending than good
behaviour bonds. Many, however, still regard suspended
sentences as a useful alternative to prison. Some even argue
that their abolition would result in a dramatic increase in the
rate of imprisonment.
Table 1 presents the results of our regression analysis which
assesses the relationships between the total number receiving
a sentence of imprisonment (FTP) with the total number of
proven offenders (PO) and the total number given a suspended
sentence (SS).
The coefficient measuring the effect of suspended sentences
(SS) on imprisonments is positive, significant and large. It tells
us that, for every 10 additional persons given a suspended
sentence, approximately 3.6 receive a full-time sentence of
imprisonment. The variable measuring the effect of the total
number of proven offenders on the number going to prison is
also (as one would expect) positive and significant. Its effects,
however, are much weaker; with every 20 additional proven
offenders resulting in just one additional person being sent
to prison. The negative coefficients on the monthly dummies
indicate that the number receiving a prison sentence is
significantly higher in December than it is in any other month
except November, where the difference does not reach
statistical significance.
Gelb (2013), for example, has argued that abolishing wholly
suspended sentences in Victoria would add approximately
5,500 people to the corrections population, including both
prison and community corrections. While Gelb acknowledges
that most offenders currently receiving suspended sentences
in Victoria would not, if the sanction were abolished, end up
receiving prison sentences, she notes that some proportion will
inevitably end up in prison. Given the social and financial costs
of imprisonment, Gelb suggests that suspended sentences be
retained to provide a ‘full complement of sentencing tools’ to
magistrates.
4
The fact that suspended sentences are being imposed on
offenders who would not otherwise have gone to prison was
what led McInnis and Jones (2010) to express concern about
their potential effects on the prison population. The present
study lends weight to their concerns. Our findings suggest
that, far from reducing the rate of imprisonment, suspended
sentences have increased it. This suggests that one way of
reducing the rate of imprisonment is to abolish or curtail the use
of suspended sentences in favour of sanctions (e.g. community
service orders) that, if breached, do not automatically result in
imprisonment.
As with all regression analyses, our conclusion regarding the
effect of suspended sentences on the rate of imprisonment is
subject to a number of caveats. The most important of these is
the assumption that we have not omitted any factor that might
have induced a correlation between suspended sentences
and imprisonment. One factor that might appear to breach
this assumption is a change in the seriousness of offending. A
general increase in the seriousness of offending (even without
any increase in the total number of proven offenders) would
cause both the number of persons given suspended sentences
and the number of persons given a prison sentence to increase.
This would create the spurious impression that the former was
causing the latter.
Fortunately, the current study is not vulnerable to this
problem. It will be recalled that, rather than analyse the
relationship between suspended sentences, proven offenders
and imprisonment in levels (i.e. using the raw time series of
each), we analysed the series in differences so that they were
stationary. This had the effect of removing the trend from each
series, leaving only the month to month variation for analysis.
Removal of the trend in our dependent and independent
variables would have removed the effect of any general
increase in the seriousness of offending.
References
Bartels, L. (2007). The Use of Suspended Sentences in Australia:
Unsheathing the Sword of Damocles, Criminal Law Journal, 31,
113-132
Box, G. E., Jenkins, G. M., & Reinsel, G. C. (2013). Time series
analysis: forecasting and control. Hoboken, New Jersey. John
Wiley & Sons.
Gelb, K. (2013). The Perfect Storm? The Impacts of Abolishing
Suspended Sentences in Victoria. Report prepared for Catholic
Social Services in Victoria. Available at: http://www.css.
org.au/Portals/51/The%20Perfect%20Storm%20-%20
The%20Impacts%20of%20Abolishing%20Suspended%20
Sentences%20in%20Victoria,%2011%20December%202013.pdf
Ljung, G.M. & Box G. E. (1978). On a measure of lack of fit in time
series models. Biometrika, 65(2), 297-303.
McInnis, L. & Jones, C. (2010). Trends in the use of suspended
sentences in NSW. Bureau Brief, 47. Sydney: NSW Bureau of Crime
Statistics and Research.
Shapiro, S.S. and Wilk, M.B. (1965). An analysis of variance test
for normality (complete samples). Biometrika, 52(3-4), 591-611.
Weatherburn, D. & Bartels, L. (2008). The recidivism of offenders
given suspended sentences in New South Wales. Australia.
British Journal of Criminology, 48(5), 667-683.
NSW Bureau of Crime Statistics and Research - Level 8, St James Centre, 111 Elizabeth Street, Sydney 2000
[email protected] • www.bocsar.nsw.gov.au • Ph: (02) 9231 9190 • Fax: (02) 9231 9187 • ISBN 978-1-921824-87-6
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